The paper presents results on acousto-optic investigation of unusual acoustic phenomena taking place in crystals possessing strong anisotropy of elastic properties. Advantages of the applied method of analysis are demonstrated by the example of the commonly used acousto-optic material tellurium dioxide. The major goal of the research consists of experimental verification of theoretical conclusions related to peculiar cases of acoustic propagation and reflection recently observed in the crystalline material. In particular, the case of glancing incidence and the following reflection of elastic energy from a free boundary separating the paratellurite crystal and the vacuum is examined in the paper. It is shown in the acousto-optic experiment that, in the case of glancing incidence, energy flow of a reflected acoustic wave may propagate practically in a reverse direction with respect to an incident wave. It is also proved that strong elastic anisotropy of the crystal is responsible for the unusual propagation and reflection of the acoustic waves. The research confirms the conclusion that the examined acoustic effects may be useful in development of new acousto-optic devices.